please help:
if 0 is smaller then or equal to a which is < then 2pi then the equation sina=cos a has how many solutions? what are they? justify.
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please help:
if 0 is smaller then or equal to a which is < then 2pi then the equation sina=cos a has how many solutions? what are they? justify.
Sketch the curves y=sin(x) and y=cos(x) over the interval (0, 2 pi).Quote:
Originally Posted by seb
You will observe that there are two points at which the cross, and the
x's for these points are the values for which sin(x)=cos(x) and so are
the values of a that you require.
sin(a)=cos(a)
can be rearranged to tan(a)=1, so one solution is 45 degrees (pi/4 radian)
The other solution is in the third quadrant (where tan is positive) and so
is 180+45 degrees (pi+pi/4 radian)
RonL
Hello, seb!
Quote:
if 0 < θ < 2π, then the equation sinθ = cosθ has how many solutions?
What are they? .Justify.
Divide both sides by cosθ, and we have: .tanθ .= .1
The only angles on the inteval [0, 2π) with a tangent of 1 are: .π/4 and 5π/4
Therefore, there are two solutions: .θ .= .π/4, 5π/4